Question 60870: The recent average starting salary for new college graduates in computer information systems is $47,500. Assume salaries are normally distributed with a standard deviation of $4,500.
a) What is the probability of a new graduate receiving a salary between $45,000 and $50,000?
b) What is the probability of a new graduate getting a starting salary in excess of $55,000?
c) What percent of starting salaries is no more than $42,250?
d) What is the cutoff for the bottom 5% of the salaries?
e) What is the cutoff for the top 3% of the salaries?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The recent average starting salary for new college graduates in computer information systems is $47,500. Assume salaries are normally distributed with a standard deviation of $4,500.
a) What is the probability of a new graduate receiving a salary between $45,000 and $50,000?
Convert the 45000 and the 50000 to z-scores
Then find the probability that z lies between those scores, as follows:
P(45000
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b) What is the probability of a new graduate getting a starting salary in excess of $55,000?
Convert 55000 to its z score.
P(X>55000)=0.048
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c) What percent of starting salaries is no more than $42,250?
P(X<=42,250)= 0.1216...
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d) What is the cutoff for the bottom 5% of the salaries?
Find the z corresponding to lowest 5%; z=-1.645..
Solve for X using z=[X-47500]/4500]
X= $40,098.16
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e) What is the cutoff for the top 3% of the salaries?
The corresponding z score is 1.88
X=4500*(1.88)+47500=$55,963.57
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Cheers,
Stan H.
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